Research in optical implementations of neural networks has included (1) systems with one-dimensional arrays of neuron units with two-dimensional interconnections and (2) systems with both one- and two-dimensional arrays of neuron units with three-dimensional volume interconnection media. The former approach does not appear suitable, due to inability to scale up to significantly larger networks than those implementable using electronics. The latter approach is currently under active investigation in a number of laboratories.
Much of the optical research has been very creative and has added important elements to an understanding of optical neural network implementations. Notwithstanding this, however, the current status is that most three-dimensional optical implementations have been specific to one neural network model, usually an associative memory. To the best of the inventors' knowledge, none have demonstrated both positive and negative weights efficiently in a working, scalable system and none have demonstrated a learning system with a large number of neuron units and independent interconnections with high connectivity (i.e., with the number of independent interconnections much greater than the number of neuron units).
In any system involving large numbers of operations, such as neural networks, telecommunications interconnections for long distance switching, and interconnections in digital computing, it is desirable to use multiplexed volume (thick) holography for storage of the interconnections, since this permits the storage of much more information than can be done in planar (thin) holograms. In the case of holographic optical elements, the utilization of a volume holographic medium permits the encoding of complex space-variant optical functions.
In forming multiplexed volume holograms, one of three approaches is typically taken: (1) sequential, which involves several temporally-sequenced (and hence incoherent) exposures of the hologram, done by rotating or translating the hologram (or the source beam or the object beam); (2) simultaneous and fully coherent, which involves the use of two or more mutually coherent beams, each encoded with information and serving as a reference beam for the other(s); and (3) some combination of sequential and simultaneous fully coherent.
The first approach has the major disadvantage that temporal sequencing is time-consumptive, which can be of considerable importance in applications envisioned herein, for which the number of independent interconnections that must be recorded is extremely large. Also, in many holographic recording materials, sequential exposures tend to erase previously recorded information, leading to the necessity of incorporating unwieldy programmed recording sequences in order to result in the storage of a predetermined set of interconnections.
The second approach is designed to circumvent the above sequencing difficulties, but suffers instead from the coherent recording of unwanted interference patterns (holograms) that give rise to deleterious crosstalk among the various (supposedly independent) reconstructions, as described in more detail below.
The third approach is subject both to sequential recording time delays and the necessity for programmed recording schedules, as well as to the generation of undesirable crosstalk. As such, none of the previously employed multiplexed recording techniques allows for the generation of three-dimensional, truly independent interconnections between two or more two-dimensional planar arrays within the context of a temporally efficient recording scheme.
In all of the prior art approaches to the holographic recording of a multiplexed interconnection, two primary forms of interchannel crosstalk are encountered to a greater or lesser extent. Coherent recording crosstalk arises from the simultaneous use of multiple object and reference beams, all mutually coherent with each other. The mutual coherence causes additional interconnections to be formed other than those desired. Reconstruction with independently valued inputs results in the generation of output beams that cross-couple through the undesired interconnection pathways which compromises the independence of the desired interconnection channels.
A second, unrelated form of crosstalk arises due to beam degeneracy, which occurs whenever a single object beam is used with a set of reference beams to record the fan-in interconnect to a single output node (e.g., neuron unit in the case of the photonic implementation of neural networks). (Fan-in is the connection of multiple interconnection lines to a common output node.) This latter form of crosstalk is present even when the set of object beams is recorded sequentially.
Of at least equally serious consequence is the optical throughput loss that results from interconnection fan-in so constructed as to exhibit beam degeneracy. In many well-documented cases, this loss is severe, resulting in at least an (N-1)/N loss (or, equivalently, a 1/N throughput efficiency) for the case of an N-input, N-output interconnection system, as reported by J. W. Goodman, Optica Acta, Vol. 32, pages 1480-1496 (1985). This is a truly daunting loss factor for interconnection systems such as those envisioned for neural networks, which may both require and be capable of 10.sup.5 to 10.sup.6 inputs and outputs.
In the prior art, few attempts have been made to address the extremely important technological problem of duplicating the contents of a fully recorded, heavily multiplexed volume holographic optical element or interconnection device, particularly in the case of neural network interconnections. For example, to the inventors' knowledge, there is no known prior technique for rapid copying of a volume hologram that is angularly multiplexed in two dimensions.
In the case of neural network interconnections, the training and/or learning sequences may be quite involved; in some cases, the training and/or learning sequences may result in a unique interconnection, which may not be reproducible in and of itself at all. In such cases, it is desirable to replicate the contents of the interconnection medium in such a manner that a fully functional copy is produced, as characterized by a complete operational set of interconnections indistinguishable from those implemented from the master. The method of replication must not demand an extremely lengthy recording sequence, must not be inefficient in its utilization of the programmed recording schedule and/or the total optical energy available for reproduction purposes, and must not induce additional optical throughput loss or interchannel crosstalk beyond that already incorporated in the master.
It is to these ends of producing a method for holographically recording complex interconnection networks and holographic optical elements in a timely manner without significant interchannel crosstalk and/or fan-in loss that the invention described herein is directed.